Twigs and branches are loose impediments; so are dung (ewwww!), worms and insects. The caveats are that such things cannot be attached or growing, imbedded, or stuck to the ball.
Sand and loose soil are considered loose impediments on the putting surface. Players also have the option of calling snow or natural ice (but not frost) loose impediments or casual water. (Ice cubes are an obstruction.)
In the rulebook, loose impediments are covered in Rule 23.